Squeezing shape by another one
This is not at all a "physically accurate" simulation by any stretch, but it may be able to approximate the desired effect with a bunch of modifier trickery using a Vertex Weight Proximity and a Cast modifier.



Use the Vertex Weight Proximity to make a vertex group weight vary according to the distance to a random object, in this case a "cancer ball", then use said vertex group to drive the influence of a Cast modifier set to Sphere.

You can then dynamically adjust the size of the "cancer sphere" (and shape too) to influence the distortion of the blood vessels